- Home
- Standard 11
- Mathematics
8. Sequences and Series
easy
यदि $x$ और $y$ के बीच गुणोत्तर माध्य $G$ है, तो $\frac{1}{{{G^2} - {x^2}}} + \frac{1}{{{G^2} - {y^2}}}$ का मान है
A
${G^2}$
B
$\frac{1}{{{G^2}}}$
C
$\frac{2}{{{G^2}}}$
D
$3{G^2}$
Solution
(b) दिये अनुसार, $G = \sqrt {xy} $
$\therefore $ $\frac{1}{{{G^2} – {x^2}}} + \frac{1}{{{G^2} – {y^2}}} = \frac{1}{{xy – {x^2}}} + \frac{1}{{xy – {y^2}}}$
$ = \frac{1}{{x – y}}\left\{ { – \frac{1}{x} + \frac{1}{y}} \right\} = \frac{1}{{xy}} = \frac{1}{{{G^2}}}$.
Standard 11
Mathematics
